Are viscosity ratios of rocks measurable from cleavage refraction?

In this Questions contribution, I consider some of the accepted methods of measuring viscosity ratios in rocks, and pose a new one. For a wide range of strain and orientations, it can be shown that the bedding normal is immeasurably close to the XY plane, and this has applications to the relationship between cleavage and strain. I therefore propose that with some limitations, cleavage refraction can provide a measure of effective viscosity ratios in layered rocks. Examples show that cleavage refraction across competence contrasts yields surprisingly small viscosity ratios. This method might also provide a way of distinguishing Newtonian from non-Newtonian behaviour of rocks over time and space.